Despite its fast convergence rate, PI iterations are computationally expensive for MDPs with a large number of states. In particular, in the scenarios where \(n\)  is large the policy evaluation step is not practical as it requires the exact solution of an \(n\) -dimensional system of linear equations. An alternative is OPI, where the policy evaluation step is carried out approximately with a fixed number \(W\)  of VI steps. This number is generally selected to trade-off computational complexity and convergence rate. Notice that when \(W=1\)  we resort to VI and when \(W\rightarrow \infty \)  we resort to PI. We refer to [1]} for a thorough analysis of VI, PI and OPI.
